# EXERCISE 4.5 (Determinant)

class 12 maths exercise 4.5 ncert solution

Question 1: Find the adjoint of the matrix

Solution: Let

Then,
Thus

Question 2: Find the adjoint of the matrix

Solution: Let
Then,

Question 3:Â  Verify for

Solution: Let

Then,

Also,

Now,

Hence,

Now,

Also,

Hence,

.

Question 4: verify for

Solution : Let
Then

Also,

Now,

`

Now,

Also,

Hence,

Question 5: Find the inverse of each of the matrix (if it exist).

Solution: Let
Then,

Now,

Question 6: Find the inverse of the matrix (if it exists)

Solution: Let

Then
Now,

Therefore,

Hence,

Question 7: Find the inverse of the matrix (if it exists)

Solution: Let
Then,

Now,

Therefore,

Hence,

Question 8: Find the inverse of each of the matrix(if it exists)

Solution: Let
Then

Now,

Question 9: Find the inverse of each of the matrix(if it exists)

Solution:
Then,

Now,

Hence,

Question 10:Â  Find the inverse of the matrix (if it exists).

Solution: Let
Then, expanding

Now,

Therefore,

Hence,

Question 11: Find the inverse of the matrix (if it exists)

Solution: Let
Then,

Now,

Therefore,

Question 12: Let and verify that

Solution:Â  Let
Then,

Now,

Therefore,

Now for B

Let
Then,

Now,

Then,

Now,

Also,

Then we have,

and

Therefore,

Thus,

From (1) and (2),

Hence, proved.

Question 13: If , show that . Hence find .

Solution: Let

Therefore,

Now,

Hence, .

Now,

Thus,

Question 14: For the matrix , find the numbers and such that .

Solution: Let

Therefore,

Now, .

Hence,

Now,

From (1) and (2), we have,

Comparing the corresponding elements of the two matrices, we have:

Also,

Thus, and .

Question 15:Â

show that

Hence, find .

Solution: Let

Therefore,

And,

Hence,

Thus,

Now,

Now,

From equation (1) and (2)

Question 16: If

verify that

. Hence, find .

Solution: Let

Therefore,

And

Now,

Thus,

Now,

Now,

From equations and

Question 17: Let be a non-singular square matrix of order . Then is equal to:

(A)

(B)

(C)

(D)

Solution: the correct option is B.

Since be a non-singular square matrix of order

Therefore,

Thus, the correct option is B.

Question 18: If is an invertible matrix of order 2, the is equal to:

(A)

(B)

(C) 1

(D) 0

Solution: Thus, the correct option is B.

Since is an invertible matrix, exists and adj .

As matrix is of order 2, let Then,

And

Now,

Hence,

Hence,

Thus, the correct option is B.

For solution